Question

51.If A = {1, 2, 3} and B = {4, 5), then
(a) (4, 1) E AB (b) (2, 5) € AXB
(c) (1,4) EBA (d) none of these

Answer 1

Answer:

A = {1, 2, 3}, B = {4} and C = {5} (i) A × (B ∪ C) = (A × B) ∪ (A × C) Let us consider the LHS (B ∪ C) (B ∪ C) = {4, 5} A × (B ∪ C) = {1, 2, 3} × {4, 5} = {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)} Then, RHS (A × B) = {1, 2, 3} × {4} = {(1, 4), (2, 4), (3, 4)} (A × C) = {1, 2, 3} × {5} = {(1, 5), (2, 5), (3, 5)} (A × B) ∪ (A × C) = {(1, 4), (2, 4), (3, 4), (1, 5), (2, 5), (3, 5)} ∴ LHS = RHS (ii) A × (B ∩ C) = (A × B) ∩ (A × C) Let us consider the LHS: (B ∩ C) (B ∩ C) = ∅ (Here, no common element) A × (B ∩ C) = {1, 2, 3} × ∅ = ∅ Then, RHS (A × B) = {1, 2, 3} × {4} = {(1, 4), (2, 4), (3, 4)} (A × C) = {1, 2, 3} × {5} = {(1, 5), (2, 5), (3, 5)} (A × B) ∩ (A × C) = ∅ ∴ LHS = RHS (iii) A × (B − C) = (A × B) − (A × C) Let us consider the LHS: (B − C) (B − C) = ∅ A × (B − C) = {1, 2, 3} × ∅ = ∅ Then, RHS (A × B) = {1, 2, 3} × {4} = {(1, 4), (2, 4), (3, 4)} (A × C) = {1, 2, 3} × {5} = {(1, 5), (2, 5), (3, 5)} (A × B) − (A × C) = ∅ Thus, LHS = RHSRead more on Sarthaks.com - https://www.sarthaks.com/650923/if-a-1-2-3-b-4-c-5-then-verify-that-i-a-x-b-c-a-x-b-a-x-c-ii-a-x-b-c-a-x-b-a-x-c?show=650929#a650929

Step-by-step explanation:

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